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A cell-free massive multiple-input multiple-output (MIMO) network-assisted full-duplex (NAFD) system has been proposed to satisfy the exploding demand of higher data transmission speed and more efficient communication. However, a growing number of users in a cell-free system inevitably leads to pilot contamination. In this paper, we analyze the ergodic spectral efficiency of cell-free massive MIMO NAFD system in the presence of pilot contamination. The cell-free massive MIMO NAFD system model has been investigated and both uplink and downlink channel state information (CSI) is estimated under spatially correlated channels. Under pilot contamination, the closed-form sum-rate expressions of the uplink with maximum ratio combination (MRC) receiver while downlink with maximum ratio transmission (MRT), and uplink with zero-forcing (ZF) receiver while downlink with ZF precoding schemes are derived based on large-scale random matrix theory. Numerical results show that under several environmental settings, the theoretical results match well with the simulated results and cell-free massive MIMO NAFD system has a better performance than time-division duplex (TDD) system. Moreover, simulation results show that the achievable sum-rate of using ZF/ZF could be more spectrally efficient compared to MRC/MRT because of its interference suppression capability.

Spectral Efficiency of Network-Assisted Full-Duplex for Cell-Free Massive MIMO System Under Pilot Contamination